How can I navigate my scene FPS style similar to how Unity does?
The latest version of Blender has Walk Mode, You can access it by pressing Shift~ (the tilde/backtick key above Tab) or View > Navigation > Walk Navigation. If you want to use Fly Mode (which used to be the default), you can switch between them in User Preferences > Input.

Under 2.8+ you can access both from the 3D View header menu View > Navigate > Walk or Fly:



It's WASD just like in FPS-games, Q and R to move up/down. G or Tab enable gravity and collision, and V to jump in gravity mode. Space teleports you to the surface you are pointed at. You can even change the key-bindings to enable FPS Walk (the official name) on MMB down, and confirm on MMB up to always rotate (or rather: look) in FPS-style - or even hold MMB down and use WASD!